# Uncertainty Propagation in XAI: A Comparison of Analytical and Empirical Estimators

arXiv: https://arxiv.org/abs/2504.03736 · HTML: https://mlsanity.com/paper/2504.03736/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 28 references that are in the map.
- First posted on arXiv 1 Apr 2025.

## Builds on (most cited first, 20 of 20)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [The (Un)reliability of saliency methods](https://mlsanity.com/paper/1711.00867/) (2017)
- [Not Just a Black Box: Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1605.01713/) (2016)
- [CRAFT: Concept Recursive Activation FacTorization for Explainability](https://mlsanity.com/paper/2211.10154/) (2022)
- [Quantus: An Explainable AI Toolkit for Responsible Evaluation of Neural Network Explanations and Beyond](https://mlsanity.com/paper/2202.06861/) (2022)
- [Debugging Tests for Model Explanations](https://mlsanity.com/paper/2011.05429/) (2020)
- [Reliable Post hoc Explanations: Modeling Uncertainty in Explainability](https://mlsanity.com/paper/2008.05030/) (2020)
- [CXPlain: Causal Explanations for Model Interpretation under Uncertainty](https://mlsanity.com/paper/1910.12336/) (2019)
- [A Theoretical Explanation for Perplexing Behaviors of Backpropagation-based Visualizations](https://mlsanity.com/paper/1805.07039/) (2018)
- [BayLIME: Bayesian Local Interpretable Model-Agnostic Explanations](https://mlsanity.com/paper/2012.03058/) (2020)
- [Quantifying Interpretability and Trust in Machine Learning Systems](https://mlsanity.com/paper/1901.08558/) (2019)
- [Why are Saliency Maps Noisy? Cause of and Solution to Noisy Saliency Maps](https://mlsanity.com/paper/1902.04893/) (2019)
- [Xplique: A Deep Learning Explainability Toolbox](https://mlsanity.com/paper/2206.04394/) (2022)
- [CoProNN: Concept-based Prototypical Nearest Neighbors for Explaining Vision Models](https://mlsanity.com/paper/2404.14830/) (2024)

## Built on by (most cited first, 6 of 6)

- [UbiQTree: Uncertainty Quantification in XAI with Tree Ensembles](https://mlsanity.com/paper/2508.09639/) (2025)
- [UbiQVision: Quantifying Uncertainty in XAI for Image Recognition](https://mlsanity.com/paper/2512.20288/) (2025)
- [No Single Metric Tells the Whole Story: A Multi-Dimensional Evaluation Framework for Uncertainty Attributions](https://mlsanity.com/paper/2603.24524/) (2026)
- [Uncertainty Gating for Cost-Aware Explainable Artificial Intelligence](https://mlsanity.com/paper/2603.29915/) (2026)
- [ConformaDecompose: Explaining Uncertainty via Calibration Localization](https://mlsanity.com/paper/2604.27149/) (2026)
- [A Hierarchy of Entropy-Shapley Games for Multivariate Predictive Uncertainty](https://mlsanity.com/paper/2609.35217/) (2026)

## Abstract (arXiv)

Understanding uncertainty in Explainable AI (XAI) is crucial for building trust and ensuring reliable decision-making in Machine Learning models. This paper introduces a unified framework for quantifying and interpreting Uncertainty in XAI by defining a general explanation function eθ(x, f) that captures the propagation of uncertainty from key sources: perturbations in input data and model parameters. By using both analytical and empirical estimates of explanation variance, we provide a systematic means of assessing the impact uncertainty on explanations. We illustrate the approach using a first-order uncertainty propagation as the analytical estimator. In a comprehensive evaluation across heterogeneous datasets, we compare analytical and empirical estimates of uncertainty propagation and evaluate their robustness. Extending previous work on inconsistencies in explanations, our experiments identify XAI methods that do not reliably capture and propagate uncertainty. Our findings underscore the importance of uncertainty-aware explanations in high-stakes applications and offer new insights into the limitations of current XAI methods. The code for the experiments can be found in our repository at https://github.com/TeodorChiaburu/UXAI